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meteorological stations and stations ceased to exist in the first half of the 1990 year. That is way in this

work we used the database of indirect water level observations as well as climate reanalysis database.

Key modeling concept has based on implementation of a simple Decision Tree model in case of regression task (Ayzel, 2017; Breiman et al., 1984).

Typical Decision Tree model is a «white box» consists of the range of boolean classifiers which split our samples to tiny «leaf» nodes where all samples

constantly refers to the one target value (Hastie et al., 2005). Single tree-based implementation of Decision Tree is algorithm faced with the case of overfitting and robustness lack that lead to limited using in real world examples (Freund, Schapire, 1997). In our work, we used three cutting-edge machinelearning techniques based on ensemble approach to predictions: Random Forest, Extra Trees and Gradient Boosting (Ayzel, 2017; Mason et al., 2000; Zhang,Hsieh,2017).Allofthemarebasedongroup of simple Decision Tree models and provide useful trick such bagging, bootstraping, prunning etc. that totally reduce overfitting and make our models suitable to provide robust dynamics (Friedman, 2001; Kohavi, 1995; Schapire, Freund, 2012).

Materials and methods

The research material has selected as the analysis period from 2002 to 2014, all daily (reanalysis) and decadal (water level) measurements have taken to monthly values. Below is given more specific description of used the data:

1.Sea level variability based on satellite altimetry data from 1992 to 2014 (decadal values), DAHITI project (Schwatke et al., 2015);

2.River runoff of Syrdarya river (gauging station Kazaly), historical monthly values from 19791986, Global Runoff Data Center (GRDC) (www. bafg.de);

3.Atmospheric forcing: reanalysis Era-Interim, resolution 1x1 degree, daily values (Deeetal., 2011).

Ahypsometric relationship between the sea surfacelayerandthewatervolumewasobtainedforthe entire range of sea level variability according to the

DAHITI data for the period under research based on adetailedbathymetricmapoftheSmallAral(Izhitskiy et al., 2016b).

As a model linking the average monthly rates of fluctuations in climatic characteristics with the dynamics changeability of river runoff values (Ayzel and Izhitsky, 2016), a regression model of solving trees was chosen, which in general is a nonparametric model of machine learning - a simple model of the “white box” solutions, which can be described by a set of simple Boolean functions.Advantages of the regression model of decision trees are: interpretability,quicklearning,hightoleranceforincomplete data. As shortcomings, usually distinguished: high ability to retrain, instability with the dominance of one decisive class, the difficulty of finding the exact structure of the tree.

Results and discussion

Based on the described method, two statistical models were developed: a model which shows dynamic changeability of water level corresponding changes of water volume of Aral Sea and the variability forecast of the water volume of the Small Aral. In the first model, the predictors used air and precipitation values for the current and previous six months averaged over the entireAral Sea basin.The model was trained on the period from July 1979 to December 1985 according to the monthly values of theriverrunoffatthegaugingstationKazaly(Figure 3). As a result, it was used to simulate river runoff values for the period from January 1986 to September 2015 - for this period, the actual measurements of the river runoff were not available (Fig. 4).

These data, together with reanalysis data (air temperature, wind speed, precipitation) were used to train the second statistical model for predicting

Small Aral volume fluctuations on satellite altimetry data for the period from October 1992 to November 2014 (Fig. 5).

In conclusion, a modelling was made for the monthly values of the SmallAral Sea water volume

for 2015 (Figure 6). Analysis of the significance of the signs showed that the parameters of mean temperature, precipitation amount and total evaporation are most significant for the results of constructing the model of decision trees, so only they were chosen as changeability of the final model - this made themodellesssusceptibletonoise(robust),andalso minimized the risk of retraining.

Annual river runoff of Syrdaria River in the lower reaches over a long period of time is characterized by instability, which is due to both natural and anthropogenic factors. At present, the influence of the anthropogenic factor on the natural ecological system is very large. One of the main negative factors is the irrational use of water infrastructure.

The Syrdarya River in the first half of the last century was significantly regulated. Since then, the largest monthly water discharge has been characteristic of the beginning of spring, the minimum - for the entire summer period.

This distribution of river runoff is due to large volumes of water for irrigation of agricultural fields in the upper and middle reaches. Spring floods in the lower reaches of the river. The Syrdarya usually begins in late March - early April.Then, in connection with the filling of overlying reservoirs and water intakes, a recession begins in April.

The lowest monthly water discharges (in some years - 6-10 m3/s) at the mouth of the river (Kazaly gauging station) has observed in the summer months, when irrigation of agricultural land is in full swing.

Water discharge, m3/s

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0

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2006

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Water discharge, m3/s

500

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The dynamics of the average monthly annual runoff in the lower Syrdaria River is following: the loss of river runoff in the section from Kazaly to Karatereni (86 km), depending on the month, ranged from55to358m3.Suchadifferencebetweenrunoff at the Kazaly and Karateren hydroelectric facilities is associated with the filling of lakes in the coastal zone. Losses associated with the transformation of runoff in the riverbed and floodplain of the river are to a large extent recoverable, if we consider not a short time interval, but a long period during which the water of detention in the section can drain through the lower closure target. Along with such losses, there are irretrievable losses of water in the area under consideration for filling numerous floodplain lakes and old lakes that do not communicate with the river, infiltration into the soil in the floodplain and evaporation.

Lower Syrdaria River in the second half of the last century, acutely felt a shortage of water, and about 30 years ago, runoff at its mouth decreased almost to zero. However, at the end of the 80s on the territory of the former USSR, people’s views on the state of the environment changed dramatically, and the Syrdaria River delta became more careful about waterresources.Asaresult,alreadyintheearly90s, water along the river. The Syrdaria River began to flow regularly into the northern part of theAral Sea. Although the volume of this water was about 2-4 times less than the amount of natural runoff (14.9 km3), it was enough to flood a significant part of the modern “SmallAral” and there the desalination process began.

Conclusion

As a result, it should be noted that despite the serious shortage of these direct measurements of the main components of the water balance, such as the sea surface level and river runoff, the proposed method makes it possible to accurately predict the volume of waters of the Small Aral on the basis of open databases. The introduction of the factor of influence of the Kokaral dam into the model will help improve the quality of the forecast. The proposed technique can be used to obtain initial conditions in hydrodynamic simulation experiments, as well as to calculate climatic scenarios for the development of the hydrological system of the Aral Sea. Directions of further studies of the dynamics of the water volume of the Small Aral Sea are seen in the use of episodic data of field measurements for verification and more detailed adjustment of the model used,

Syrdarya for the restoration of the values of natural water inflow into the SmallAral Sea.

Acknowledgment

This work was supported by the Russian Foundation for Basic Research, project 17-05-01175 A, and the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan in the framework of the scientific Project №

AP05134202 «The current ecological state of endorheic lakes of the arid climate zone and perspectivesoftheirsustainableuse:thecaseoftheAralsea residual basins».